2.1 Review of Functions Learning Objective: to remember what a function is and what to do with it. Warm-up (IN) 1.Write down everything you think of when.

2.1 Review of Functions

Learning Objective: to remember what a function is and what to do with it.

Warm-up (IN)

1. Write down everything you think of when you hear the word “function.”

Notes!

Relation –

A set of ordered pairs

Domain – the set of all input, or x, values

Range – the set of all output, or y, values

Function –

A relation in which each value of the domain is paired with exactly one value of the range

Ex 1 – Is the relation a function?

a. 2,3 , 3, 4 , 4,1 , 1,3 yes

b. 4,4 , 2,3 , 4,2 , 3,4 1,1 no

c. D R

1 9

2 8

3 7

d. D R

1

2 5

3

e. D R

-2 4

1 5

4 -9

yes yesno

Vertical Line Test –

Used to determine if a graph is a function.

If a vertical line hits the graph no more than one time, then it’s a function

Ex 2 – Is the graph a function?

a. b. b.

yes yes no

Ex 3 – 2 2if 2 3 and , findf x x g x x x

a. 1f 2 21 3

2 1 3 2 3 5 1f

b. 2g 2 22

2 4 2 2g

c. 2 1f g 2 22 3 1 2

1

2 4 3 1 111 2 1f g

Ex 4 – Find the domain

2a. 3 1f x x x D: all real #s

5b.

3g x

x

Can’t divide by zero!

c. 2h x x

2 0x 2x

2x

2

1d. f

5 6

xx

x x

2 5 6 0x x

x x3 2

3,2x

Can’t take square root of a negative!

Switch inequality when you mult or div by a neg.

3:D x

In addition to evaluating functions at specific #s (f(2)), it is important to be able to evaluate functions at expressions that involve 1 or more variables.

the difference quotient is studied extensively in calculus f x h f x

h

Ex 5 – 2for 2 7, find f a h f a

f x x xh

Replace x with a 2 2 7f a a a Replace a with a+h 2

2 7f a h a h a h

2a 2ah 2h 2a 2h 7

f a h f a

h

2 22 2 2 7a ah h a h 2 2 7a a

h

2ah 2h 2h

h h (2a h 2)

h

2 2a h

HW – pg. 18-19, #2-48 even, 74, 76, 81

Out –

Summary – I’m glad I remember _______ or I wish I remembered ______ about functions.

Don’t forget about POW!!

2if 6 2, find 3f x x x f